# Full text of "Analytical Mechanics"

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```76                        ANALYTICAL MKCIIAXIOS
rived magnitude in the fundamental magnitude which the letter represents. Thus area has two dimensions in length and zero dimension in both time and mass, while momentum has one dimension in mass, one dimension in length, and minus one dimension in time.
75.   Homogeneity of Equations. — Magnitudes of different dimensions can neither be added nor subtracted.    Therefore in a true equation the sum of the magnitudes of one kind which are on the left of the equation sign equals the sum of the magnitudes of the same kind which are on the right.   When all the terms of an equation have the same dimensions the equation is said to be homoycncous.
76.   Systems of Units. — The C.CJ.S. System is used  in most of the civilized countries and by scientists nil over the world.   In this system the centimeter, the grant, and the second are the fundamental write.
English-speaking people use another system, known as the British gravitational system, in which weight, length, and time are the fundamental magnitude's and the pound, the foot, and the second are the fundamental units. Thus the unit of time is the same in both systems. The following equations give the relation between the centimeter and flu* inch with an error of less than one-tenth of one per cent.
1 in.   = 2.54 cms. 1 cm. = 0.3937 in.
The relation between the mass of a body which weighs one pound and the gram is given by the following equations with an error of less than one-tenth of one per cent.
1 kg. = 2.205 pds. 1 pd. « 453.0
where kg. is the abbreviation for the kilogram, or l()(K) gins., while pd. denotes the mass of a body which weighs one pound in London and is often called pound-mans. I )enot ing```